Exhaust Port Challenge

Obejctive 

1. Calculation of the wall/surface heat transfer coefficient on the internal solid surface.
2. Show the velocity & temperature contours in appropriate areas.

Introduction 

Engine exhaust port plays leading role in exust system. It connects to each exhaust port on the engine's cylinder head, and it funnels the hot exhaust to the exhaust pipe. It helps to prevents the toxic exhaust fumes from sneaking into the vehicle and harming the occupants.

Theory

Accurate calculation of convective heat transfer coefficient requires boundary condition consists of the coupling of solid and fluid fields. Such a boundary condition assumes that the heat convected in the solid is absorbed from the fluid passing over the solid surface. The heat conduction in the solid is solved by assuming a constant heat flux at solid boundary and the flow field is analyzed with the assumption of  constant wall heat flux  boundary.

To have analytical or numerical prediction of heat transfer coefficient close to experimentally obtained values, one must focus on conjugating the boundary condition at the fluid–solid interface through coupled heat transfer analysis. In such a case suitable governing equations are to be solved in the respective sub-domains and these solutions need to be conjugated at the interfaces of sub-domains.

Since the governing equations of fluid and solid domains are different, numerical treatment and solution strategy may also differ in individual solution domains. However those solutions required to be coupled at the solid-fluid interface through dynamic update of interface boundary condition. Govering equation for conjugate heat tranfer are:-

Contunity equation

`{delu}/{delx}+{delv}/{dely}=0`

2-D Momentum equation

`{delu}/{delt}+u{delu}/{delx}+v{delu}/{dely}=-1/rho{delp}/{dellx}+gbeta(T-T_{oo})+v{del^2u}/{dely^2}`

2-D Convective heat transfer equation

`{delT}/{delt}+u{delT}/{delx}+v{delT}/{dely}=alpha{del^2T}/{dely^2}+v/{C_p}({delu}/{dely})^2`

2-D Heat conduction equation

`rho_sC_s{delT_s}/{delt}=lamda_s({del^2T_s}/{delx^2}+{del^2T_s}/{dely^2})+q_v`

Conjugate heat transfer (CHT)

Simultaneous multiple heat transfer modes occur in almost all real-world problems. CHT refers to situations in which multiple modes of heat transfer occur simultaneously. It allows simulation of heat transfer between solid and fluid domains by exchanging heat enegry at their interface.

In solids, conduction often dominates whereas in fluids, convection usually dominates. Conjugate heat tranfer analysis is used to design effective HVAC, Heat Exchanger, Tank, Internal Combustion Engine, Heat Sink, Boiler, Reactor, Heat Pipe, Turbocharger etc.

Geometry

Meshing

Mesh size=0.15m

Body Mesh size=0.0155m

No. of nodes=1,70,722

No. of element=4,89,734

Inflation layers is created between the fluid and solid interface. The number of inflation layer is 5 and it's thickness is 5mm.

Simulation Setup

The simulation is run for steady and pressure based solution. K-epsilon model is used for the simulation of this kind of problem.

Boundary

Inlet air velocity=5 m/s

Inlet air temperature=700 K

outer constant heat flux wall with heat flux=20`w/{m^2-K}`

outlet gauge pressure=0 Pa

Results

Simulation get converged at around 450 iterations.

Temperature Contour

Though temperature of fluid is more at inlet but the temperature of solid surface is more in outlet pipe due high mass flow rate of fluid.

Velocity streamline curve

Maximum velocity is about 41 m/s. Velocity in outlet pipe is high due to high mass flow rate.

Heat Transfer Coefficient

The heat transfer coefficient is varies between 72.2-220.5 `W/{m^2K}`.

Verification of Results

There are two ways to varify the results of simulation

1. Conduct an experiment with similar condition and record the essential data which can be used to calculate heat transfer coefficient.                                                 `(Nu=0.023*Re^0.8*Pr^0.4)`                                                                                                  and `Nu={hl}/k`
2. Conduct grid independency test by varying the mesh size and compare the results. 

Factors affecting the accuracy of the prediction

1.  Mesh size and fitting:- Finer the mesh more accurate is the result. Mesh element should be precise around the curvature.
2. Inflation layer:- Inflation layer at the interface between fluid and solid.
3. Share topology:-Mesh should be spherically symmetric to smooth mesh transition in various areas.